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Unformatted text preview: HOMEWORK ASSIGNMENT 10 PHYS852 Quantum Mechanics II, Spring 2009 New topics covered: partial waves, scattering resonances . 1. Hardsphere Swave scattering: Consider Swave scattering from a hard sphere of radius a . Make the ansatz ψ ( r,θ,φ ) = e ikr r (1 + 2 ikf ( k )) e ikr r and show that it is an eigenstate of the full Hamiltonian for all r > a . Fit the value of f ( k ) to satisfy the boundary condition ψ ( a,θ,φ ) = 0. What is the partial amplitde f ( k )? What is the swave phaseshift δ ( k )? 2. Hardsphere Pwave scattering: For Pwave scattering from a hard sphere of radius a , make the ansatz ψ ( r,θ ) = bracketleftbiggparenleftbigg 1 kr i ( kr ) 2 parenrightbigg e ikr + (1 + 2 ikf 1 ( k )) parenleftbigg 1 kr + i ( kr ) 2 parenrightbigg e ikr bracketrightbigg Y 1 ( θ ) , and show that it is an eigenstate of the full Hamiltonian for r > a . Again solve for the partial amplitude f 1 ( k ) by imposing the boundary condition ψ ( a,θ ) = 0. What is the phaseshift) = 0....
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This note was uploaded on 10/25/2010 for the course PHYSICS PHYS 851 taught by Professor Michaelmoore during the Fall '08 term at Michigan State University.
 Fall '08
 MichaelMoore
 mechanics, Work

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